Absolute Value Inequalities Worksheet

The transformational approach extends the initial conceptual understand-. 3 Solving & Graphing Absolute Value Inequalities Lesson 2. If “and” was used, the solution set is the set of all numbers in both solution sets of the two inequalities. Solving Absolute Value. Absolute Value Inequalities. So when we combine absolute values and. Y Worksheet by Kuta Software LLC Math 120 ID: 1 Name_____ Review Sheet: Inequalities Date_____ Draw a graph for each inequality. Solving and Graphing Inequalities Worksheets Linear inequality worksheets contain graphing inequalities, writing inequality from the graph, solving one-step, two-step and multi-step inequalities, graphing solutions, solving and graphing compound inequalities, absolute value inequalities and more. Example: Solving Inequalities Using Addition/Subtraction. com Informal together with formal feedback sessions help do away with splinters that may hamper the practice of achieving the vision. Worksheet by Kuta Software LLC Algebra 1 Review: Absolute Value Equations and Inequalities Name_____ ID: 1 Date_____ Period____ ©A o2U0Y1l5g wKmuctUaR zSqoPf\tTw^ahr. Case 1 : The expression inside the absolute value symbols is positive. -value < expression < value This is a basic property of absolute value inequalities that needs to be memorized. Since it is a distance, it is always positive. Absolute Value Inequalities Worksheets. They are solved differently. This topic covers: - Solving absolute value equations - Graphing absolute value functions - Solving absolute value inequalities Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Isolate the absolute value: expression number 2. On the number line above, notice that -3 is a line. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. To show that we want the absolute value of something, we put "|" marks. Separate – 1 ≤ x + 3 < 8 into two different inequalities and then graph the indicated values of x on a number line. This quiz and worksheet give you the chance to quiz yourself on absolute value inequalities. 5 Absolute Value Equations. You've been inactive for a while, logging you out in a few seconds. Write an absolute value inequality that describes the possible lengths of a standard basketball court. Developmental Mathematics II Linear Inequalities Name_____ MULTIPLE CHOICE. Multiplying Absolute Value Worksheets. Grade level: 9-12 Age range: 15-19 This lesson demonstrates how to solve Absolute Value Inequalities. 50 and each kickboard costs $10. You are asked to buy some small decorative pumpkins to bring to a Halloween party. There are 10 inequalities total, including many in which the absolute value must be isolated. In both cases, their absolute values will both equal positive 3. It is presented in a number line. Worksheet Adding And Subtracting Fractions. Vertical Line Test - is a test to see if the graph represents a function. Here is your free content for this lesson! Absolute Value Equations and Inequalities - Word Docs & PowerPoints To gain access to our editable content Join the Algebra 2 Teacher Community!Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards. These printable worksheets can be used to teach your students about the absolute value of integers. Absolute Value Step-by-step Lesson- We start solving real life banking problems. We have the following theorem from Intermediate Algebra to help us. ) From here on out I am unsure or the answers. The pattern for "greater than" absolute-value inequalities always holds: the solution is always in two parts. For example, use mult instead of multiply or multiplication to find worksheets that contain both keywords. Personalized Help ($): Investigate hiring a qualified tutor in your local area (US only), or try e-mail tutoring from Purplemath's author. Solve the compound inequality 6x-4<-34 or 3x +10>10 I think the answer is x<-5 or x>0 b. Write an inequality for the scenario. −2 < x < 4 26. 5, including-1. The exactly dimension of Agreeable solving Absolute Value Equations and Inequalities Worksheet Also Algebra 2 Worksheets was 612x792 pixels. f P VAel plB erUivg kh3t WsZ hr beqs Ee qr fv 4e Qdj. If it is possible to solve the inequality algebraically, do so and give exact solutions. a) The student will solve absolute value equations and inequalities. • Do you UNDERSTAND? Reasoning When is the absolute value of a number equal to itself? 27. Solve Absolute Value Inequalities Worksheet Free Worksheets from Absolute Value Inequalities Worksheet, source:comprar-en-internet. How do you set up absolute value inequalities when you solve. Graphing absolute value functions or equations, examples: Quadratic equations with absolute value: Graphical interpretation of the definition of the absolute value of a function y = f (x) will help us solve an equation with absolute value. How To Find The Domain of a Function - Radicals, Fractions & Square Roots - Interval Notation - Duration: 18:45. Absolute Value Math Word Problems. l M EASltlg zrXiogMhYtxsz OrkegsLerr\vyeAdB. Isolate the absolute value. Absolute Value Inequalities. Case 2: The expression inside the absolute value symbol is negative. Solving equations or inequalities involving absolute values is based on the definition of absolute value. General Formula for Absolute Value Inequality Graph and Solution. fx jx < 6 or x > 2g D. Which equation states that the temperature, t, in a room is less than 3 from 68 ? A. Related SOL: AII. worksheets about modeling with linear equations. ©D t2 7021 B2O 1Kcuft XaP QSmoMfft vw5a5rdeR 8L sL BCo. Learn absolute value 2 inequalities with free interactive flashcards. These printable worksheets can be used to teach your students about the absolute value of integers. Algebra worksheets to improve student performance through fun riddles, activities and games. Worksheet given in this section will be much useful for the students who would like to practice problems on solving absolute value inequalities worksheet. p < -8 and p > 4. x += 5 15 0 x += is equivalent to. Showing top 8 worksheets in the category - Absolute Value Inequalities. Systems of Equations and Inequalities. During the day, the temperature varied from this by as much as 7. The compound statement can then be solved and the solution set can be graphed or expressed in interval notation. Solving Linear Inequalities. The solution will be all points that are more than two units away from zero. Solving Absolute Value Equations and Inequalities Worksheet We collect this best photo from internet and choose one of the best for you, you can see Solving Absolute Value Equations And Inequalities Worksheet and more pictures selection that posted here was carefully picked and uploaded by admin after selecting the ones that are best among the others. 0 Equation Picture Objectives The student will be able to: What is the difference between and and or? PowerPoint Presentation PowerPoint Presentation 3) Which inequalities describe the following graph? 4) Graph the compound inequality 6 : m 8 5) Which is equivalent to -3 y 5? 6) Which. Related SOL A. This way of thinking about absolute value is enormously helpful in understanding inequalities that involve absolute values. ©s cKfuftwa0 NSboqfst3woaPrCeY 7LELJCh. I am passionate about travelling and currently live and work in Paris. --- 2 The absolute value of 6 - x will remembering to reverse the inequalities when dividing by. It includes both addition and subtraction of absolute value of integers. Class Notes Linear Inequalities. Inequalities and Absolute Values The fields at the right may be moved by the mouse into any of the empty marked positions. It explains what is the absolute value of a number and includes problems with number lines, greater than and less than, and solving simple expressions. 8 Absolute Value Inequalities Problems Practice Worksheet College Algebra 2 doc pdf. Which inequality represents all possible lengths of the box? A) x −0. Check by substituting into the original equation. Calculate the absolute value of numbers. a less than) is very different from solving an inequality with a > (i. Absolute Value Inequality WS. Express each statement using an inequality involving absolute value. Showing top 8 worksheets in the category - Absolute Value Inequalities. 3 - Absolute Value Inequalities. j68+tj< 3 12. Algebra Help Absolute Value Equations Elmifermetures Com. 3 (Compound Inequalities; Absolute Value Equations and Inequalities) has been split into two sections (1. The solution is the intersection of the solutions of these two cases. Graph the functions y = │x │ and y = - │x │ together on a coordinate plane. If there are 2 boundary points, the number line will be divided into 3 regions. PreCalculus Name: _____ Worksheet: Inequalities and Absolute Value. 2 – Absolute Value Equations. Absolute value inequalities. length to differ from this value by at most 0. D Worksheet by Kuta Software LLC Coordinate Algebra Name_____ Absolute Value Equations & Inequalities Review Date_____ Period____ Solve each equation. fifty-two less than three times n b. 6 Materials: Absolute Value Matching Cards activity sheet (attached) Absolute Value Equations/Inequalities activity sheet (attached) Absolute Value Stations Review activity sheet (attached) Graphing utility Colored pencils or highlighters. A worksheet is often a notepad given by an educator to students that lists tasks for the students to accomplish. Then graph. 6 OR greater than or equal to 104. Solving absolute value equations and inequalities. ©s cKfuftwa0 NSboqfst3woaPrCeY 7LELJCh. How do you describe all real numbers x that are within δ of a? (a) Graphically, as on the line above. M p gAQlVlr DrViIguh8tFsT lr 0ejs6eWrhvjezdH. 4_solving_abs_val_inequalities_preap__practice_key. Be sure to show how to represent this on a number line. j68+tj< 3 12. greater than). Absolute Value Inequalities Example 3 Absolute Value Inequalities Example 1 This original Khan Academy video was translated into isiXhosa by Sive Nobevu. PreCalculus Name: _____ Worksheet: Inequalities and Absolute Value. But they are on the SAT and that test you've got coming up, so hey, I guess they're not totally useless. This value or number represents the distance between a and 0 on a number line. The absolute value of a number is represented in the form as |a|. Solving Absolute Value. 5 P 2Aflhlp Ir5i sg Jh3t Is m yrPecs2earqvBewdU. Often times, the interviewer could possibly ask quite possibly the most frustrating issues, which throw the interviewee off equilibrium and obtain him anxious. The "Reset" button restores the original situation, the movable fields being placed at random positions. Class Notes Absolute Value Inequalities (Combined w/ 2. This lesson focuses on solving absolute value inequalities. Absolute value is simply a measure of how far an integer is from zero on a number line. Improve your math knowledge with free questions in "Solve absolute value inequalities" and thousands of other math skills. The absolute value of a negative number is the opposite number (the same numeral but without the minus sign in front of it). It is presented in a number line. Subtracting Absolute Value Worksheets. The absolute value of a number can’t be negative. If all terms of an inequality are absolute values then the only way either side could be negative is if the collection of terms on that side contained a subtraction. 62/87,21 Since within implies that the pH can be up to 0. 1) 5 - 3n > -10 or 5n - 5 ³ 352) -9k + 7 ³ 16 and 5 - k £ 13. 1 - Compound Inequalities. 1 – Expressions and Formulas. Solve absolute value equations and inequalities. But they are on the SAT and that test you've got coming up, so hey, I guess they're not totally useless. You've been inactive for a while, logging you out in a few seconds. Write an absolute value inequality describing the range of possible depths for green plants in an ocean. Before look at the worksheet, if you would like to know the basic stuff about solving absolute value inequalities,. ← Solving Algebraic Equations Free Solving Absolute Value Equations And Inequalities Algebraically Worksheet Answers → Leave a Reply Cancel reply Your email address will not be published. Normally absolute value mean without considering the sign. Write two equations without absolute values. Keystone Review { Absolute Value & Inequalities 10. Solve Real-World Problems Using Inequalities. ©V TKhugtfaW USwo8fNt6wMaXrceW PL8L8Ct. RE-write without the absolute value sign. To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. And recall that the definition of absolute value is the distance that a value is from 0 on the number line. 3 Assign the absolute value inequality its corresponding number line. Gallery for 50 Absolute Value Inequalities Worksheet. 1 Absolute Value Inequalities. 62/87,21 Sometimes; the graph could be the intersection of two graphs, the empty set, or all real numbers. The symbols less than and greater than are the difference between the equalities and inequalities. length to differ from this value by at most 0. 62/87,21 Since within implies that the pH can be up to 0. Solve an Absolute Value Inequality (>) You can interpret |a| > 2 to mean that the distance between a and 0 on a number line is greater than 2 units. 2 Solving Equations 3 Solving Inequalities 4 QUIZ 5 Absolute Value Equations. So I can convert my last line above to the following: |. Algebra worksheets to improve student performance through fun riddles, activities and games. Solving Absolute Value Equations Examples 1. Showing top 8 worksheets in the category - Absolute Value Inequalities. Absolute value is the distance a number is from zero. Jolene hartwick wwtc, solve equations using square root property, simplest form calculator, math worksheets absolute value, casio solve equation, sats papers 1998, example problems advanced trig. Solving and graphing absolute value inequalities with two variables is also a skill that math teachers require students to master in Algebra I. notebook 1 September 16, 2014 Goal: To solve double absolute value inequalities. the direction of the inequality symbol. As a result both ten and negative ten have an absolute value of ten. Before look at the worksheet, if you would like to know the basic stuff about solving absolute value equations,. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Absolute value is simply the distance an integer is from zero on a number line. 1 Guided Notes. All the questions are relevant to all major exam boards including AQA,. 8) vertex moved left 9, up 4, opening down, compressed by a factor of 1 2. Write each compound inequality as an absolute value inequality. Subtracting Absolute Value Worksheets. Alternatively you could de ne it as jaj = + p a2. Write and solve an absolute-value inequality to find the range of acceptable lengths. On this page you will find: a complete list of all of our math worksheets relating to Precalculus. Absolute Value Calculator-- Enter expression (numbers and signs only) Absolute Value Video. Go through a couple of examples with the students, then have them complete some practice problems or a worksheet. Multiply two absolute value of integers. Chapter 2: Linear Equations and Inequalities Lecture notes Math 1010 Ex. Solving Absolute Value Inequalities - Module 2. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. 5 in either direction, the symbol to use is less than or equal to. A compound inequality combines two inequalities using either “and” or “or”. Write an inequality that demonstrates Eva's situation, then graph it. gago says:. The absolute value of a positive number is the number itself. fx jx < 6 or x > 2g D. See our article on the absolute value function for more information, as well. h Compound and Absolute Value Inequalities. NOTES –INEQUALITIES (One Variable, Linear, and Systems) ONE VARIABLE INEQUALITIES Inequality Symbols: < less than > greater than less than or equal to greater than or equal to include that Solving One Variable Inequalities: Solve inequalities the same way you would solve an equation. 6 and less than or equal to 99. D Worksheet by Kuta Software LLC Coordinate Algebra Name_____ Absolute Value Equations & Inequalities Review Date_____ Period____ Solve each equation. 2 Solving & Graphing Absolute Value Equations Lesson 2. Write and solve an absolute value inequality representing the possible range of weights of the bags of pumpkins. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars. fx j6 < x < 2g B. In the picture below, you can see generalized example of absolute value equation and also the topic of this web page: absolute value inequalities. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. 1) 5 - 3n > -10 or 5n - 5 ³ 352) -9k + 7 ³ 16 and 5 - k £ 13. 5, including-1. Absolute Value Equations. Solving equations with two absolute value. 1 Solve and Graph Simple and Compound Inequalities A3. Free worksheets for solving or graphing linear inequalities. The inequality compares an absolute value function with a negative integer. A linear equation in one variable is also called a first-degree equation. Learn absolute value 2 inequalities with free interactive flashcards. Solving Inequalities Interval Notation, Number Line, Absolute Value, Fractions & Variables - Algebra - Duration: 30:44. 2014 A Review Solutions. Many of the formulas we use in everyday life are literal equations. Vary the terms of the absolute-value function and vary the value that you are comparing it to. The graph of a linear equation is a straight line and any point in the Cartesian plane with respect to that will lie on either side of the line. 4 Inequalities with Absolute Value and Quadratic Functions 211 We now turn our attention to solving inequalities involving the absolute value. To solve an absolute value inequality, you need to use the definition of absolute value. And while normally there are 1 or 2 solutions to a multi step equation, in the form of x= #, you'll have the same thing, but with an inequality sign (or signs). Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. On this page you will find: a complete list of all of our math worksheets relating to Precalculus. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. Absolute Value Equations and Inequalities. Make your own examples of absolute value equations and inequalities that have no solution, at least one for each case described in this section. Since the absolute value of any real number is greater than or equal to 0, it can. Inequalities Graphing and Absolute Value Graphing on a Number Line; Quiz: Graphing on a Number Line; Absolute Value; Quiz: Absolute Value; Solving Equations Containing Absolute Value; Inequalities; Quiz: Inequalities; Coordinate Geometry Linear Inequalities and Half-Planes; Quiz: Linear Inequalities and Half-Planes; Coordinate Graphs; Quiz. Solve an inequality involving absolute values using a graph of the absolute-value function. Systems of Linear Inequalities; Reciprocal Functions Worksheet (done in class) 1 Response to Ch. We have the following theorem from Intermediate Algebra to help us. Graph using your calculator and leave the equation in y for the rest of the activity. Grass Fedjp worksheet Worksheet Adding And Subtracting Fractions add subtract multiply divide fractions angles worksheets dividing printable adding. worksheets about modeling with linear equations. To solve an absolute value inequality, you need to use the definition of absolute value. For example, |-27| equals 27. Now, we know that Absolute Value is the distance from zero, and an Inequality is a comparison between two or more things, and all we’re going to do is take our solving techniques from both of those lessons and put them together!. To solve an absolute value inequality, knowledge of absolute values and solving inequalities are necessary. Engaging math & science practice! Improve your skills with free problems in 'Writing Absolute Value Inequalities Given a Word Problem' and thousands of other practice lessons. z-3-Worksheet by Kuta Software LLC Answers to Absolute Value and Radical Equations and Inequalities 1) x y 2) x y. Choose a specific addition topic below to view all of our worksheets in that content area. She needs to buy a small laptop computer before the next semester. Inequalities Graphing and Absolute Value Graphing on a Number Line; Quiz: Graphing on a Number Line; Absolute Value; Quiz: Absolute Value; Solving Equations Containing Absolute Value; Inequalities; Quiz: Inequalities; Coordinate Geometry Linear Inequalities and Half-Planes; Quiz: Linear Inequalities and Half-Planes; Coordinate Graphs; Quiz. 1 – Compound Inequalities. The compound statement can then be solved and the solution set can be graphed or expressed in interval notation. On this page you will find: a complete list of all of our math worksheets relating to Precalculus. Sara goes to Fredonia University. This is the content of the following useful theorem, called the triangle inequality. Improve your math knowledge with free questions in "Solve absolute value inequalities" and thousands of other math skills. Gallery for 50 Absolute Value Inequalities Worksheet. greater than). Explanation: However, inequalities are tricky in the fact that if you multiply or divide by a negative number, you must flip the sign. Find intersections and unions of intervals. fx j2 < x < 6g C. 3 Solving & Graphing Absolute Value Inequalities Lesson 2. Share your strategy for identifying and solving absolute value equations and inequalities on the discussion board. The dot next to the choice indicates that it is the answer. 1 Guided Notes. Former Section 1. Chapter 1 Review Worksheet - Equations and Inequalities _____ Section 1. no solution. These are one-step inequalities with mostly positive integers. General Formula for Absolute Value Inequality Graph and Solution. Go through a couple of examples with the students, then have them complete some practice problems or a worksheet. Write an inequality that demonstrates Eva's situation, then graph it. both sides of an inequality by a. number, you must. discussing absolute value as a piecewise function and looking at the definition of absolute value, the distance from zero on a number line. Absolute Value Inequalities Worksheet Answers - Some will ask that you simply split the inequality. all numbers greater than 4 or less than -4 ] n[ > 4 2. Solve an inequality involving absolute values using a graph of the absolute-value function. Engaging math & science practice! Improve your skills with free problems in 'Writing and Solving Compound Inequalities Given a Word Problem' and thousands of other practice lessons. Showing top 8 worksheets in the category - Absolute Value Inequalities. Absolute Value Subtraction 2. 1) y £ -2x + 2 x y. Take all the inequalities obtained (these are all solution sets) and figure out the solution set. A worksheet is often a notepad given by an educator to students that lists tasks for the students to accomplish. Absolute value is simply the distance an integer is from zero on a number line. h Worksheet by Kuta Software LLC Algebra II - Clark ID: 1 Name_____ Date_____ Period____ ©O t2 20A152 j 6K huJt AaR TSvoUfQtRw UaDrte0 kL vL5CZ. 4 Determine the dangerous and critical temperatures. INEQUALITIES WITH ABSOLUTE VALUES. Numerical Expression Worksheets 5th Grade Best Equations from graphing absolute value inequalities in two variables worksheet pdf , source:transatlantic-news. pdf: File Size: 1947 kb:. 3 Solve 7 = 5x 2x+1. Arrow to the right to find the NUM menu. Write the inequality in words. They are the same distance from 0 on the number line, but in opposite directions. This is the Absolute Value Inequalities Worksheets section. The exactly dimension of Agreeable solving Absolute Value Equations and Inequalities Worksheet Also Algebra 2 Worksheets was 612x792 pixels. Write each compound inequality as an absolute value inequality. Recall that ∣ x ∣ = 2 means the distance between x and 0 is 2. -1-EXAMPLES: Solve each compound inequality and graph its solution. Solving equations or inequalities involving absolute values is based on the definition of absolute value. These are only relevant for the GCSE maths 9-1 higher tier exams. Absolute Value Equations and Inequalities. Write the inequality in words. greater than). Then explore how the graph and solution set change in response. Absolute Value Inequalities worksheets from absolute value inequalities worksheet , image source: www. Solving Absolute Value Equations and Inequalities Worksheet Name:_____ Solve each inequality and graph its solution on a number line. Absolute value inequalities worksheet bath county schools graphing absolute value equations dilations reflections Printable Worksheets and Activities for Teachers, Parents, Tutors and Homeschool Families. Appendix E: Absolute Value A45 is always less than or equal to the sum of the absolute values. For example, ∣ x ∣ < 2 and ∣ x ∣ > 2 are absolute value inequalities. If you answered no, then go on to step 3. Choose one topic from the chapter to explain with detail: relations and functions, linear relation and functions, rate of change and slope, writing linear equations, scatter plots and lines of regression, special functions, parent functions and transformations, or graphing linear and absolute value inequalities. Example: Solving Inequalities Using Addition/Subtraction. Knowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge. Some of the worksheets displayed are Solving absolute value equations, Solving absolute value equations and inequalities, Soving absolute value equations, Absolute value equations, Integers and absolute value study guide, Absolute value word problems homework, Mth132 absolute value. She says that her secret number is more than 11 units away from 50. Absolute Value Subtraction 1. D G BANl4la krtiJg1hAtxse NrPe3sherKvme4dK. Write an inequality that demonstrates Eva's situation, then graph it. Showing top 8 worksheets in the category - Absolute Value Equations Quiz. Solving Compound and Absolute Value Inequafities Write an absolute value inequality for each of the following. Unit 4 - Compound Inequalities and Absolute Value. 1) n 2) p 3) m. Normally absolute value mean without considering the sign. Solving inequalities with absolute values. 1) y £ -2x + 2 x y. Solving Compound and Absolute Value Inequalties - Answers #1, #2. Step 2: Use the definition of absolute value to set up the inequality without absolute values. This post provides an overview of linear, absolute value, and quadratic inequalities. Absolute Value Inequalities. When inequalities include absolute expressions,. absolute value graph inequality equation Rate how well you can use absolute value to solve equations and inequalities. Inequalities & Absolute Value ID: 1 ©t O2I0I1t8W bKBuitrai NSioMfdtowkabrgeU ALJLYC^. Absolute value inequalities can have one or two variables. This problem is like problem 1 except that we are using a instead of 0. Inequalities Reporting Category Equations and Inequalities Topic Relating the graphing of a line to solving an inequality in one variable Primary SOL A. Worksheets are used for all subjects (for example math, geography, etc. -5-4-3-2-1 012345 |−5| =5 |2| =2 |0| =0 |a−b| is the absolute value of (a−b), or the distance from a to b Example: |5−3| =2 28. Solving Absolute Value Inequalities Worksheet for 9th from solving absolute value inequalities worksheet , image source: www. We have the following theorem from Intermediate Algebra to help us. Gallery for 50 Absolute Value Inequalities Worksheet. Absolute value less than. Solve Real-World Problems Using Inequalities. Lesson: Solving Compound Inequalities Date: Period: Graph the solution set of each compound inequality. ©D t2 7021 B2O 1Kcuft XaP QSmoMfft vw5a5rdeR 8L sL BCo. Pizzazz Algebra Author: Stephanie Demaio Created Date: 20160919154753Z. Write and solve an absolute-value inequality to find the range of. Pinterest from Absolute Value Inequalities Worksheet , source: pinterest. fx jx < 2 or x > 6g 11. Similarly, 3 is also a distance of three units from zero on the number line. greater than). The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under  Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of $1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to $960 billion this fiscal year, and back over $1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: